On the global Gaussian Lipschitz space
Journal article, 2017
A Lipschitz space is defined in the Ornstein-Uhlenbeck setting, by means of a
bound for the gradient of the Ornstein-Uhlenbeck Poisson integral. This space
is then characterized with a Lipschitz-type continuity condition. These
functions turn out to have at most logarithmic growth at infinity. The
analogous Lipschitz space containing only bounded functions was introduced
by Gatto and Urbina and has been characterized by the authors.